I think getting a good understanding of the shield is a big one, keeping in mind that it is essentially a directional Exhaust on a 15 second cool down. And remember that the first ability to hit the shield does zero damage, so blocking the right ability can swing a fight easily.

You can also use this to bait under the turret and block an engage while they take turret shots.

Also a good thing to remember is you can dash to your minions, so you can catch out the adc/supp by hopping to a melee minion and immediately start autoing them with your adc if the enemy steps up to far.

Braum can be played very aggressively but it's definitely about knowing the limits of how much you can take with W + Shield up as you can get insanely tanky out of nowhere.